{
  "abstract": "FINDING: Langlands duality induces a rational isomorphism in K-theory between group C*-algebras of extended affine Weyl groups, via equivariant Poincaré duality on dual tori. MATH: Let \\( \\check{T} \\) and \\( T \\) be dual tori (Langlands dual), with finite group actions \\( W \\) (Weyl group). Construct equivariant Poincaré duality: \\( K^*_W(\\check{T}) \\cong K^{\\dim T - *}_W(T) \\) rationally. Extended affine Weyl group \\( \\tilde{W} = W \\ltimes Q^\\vee \\) (coroot lattice). Then \\( K_* (C^*(\\tilde{W})) \\otimes \\mathbb{Q} \\cong K_* (C^*(\\tilde{W}^\\vee)) \\otimes \\mathbb{Q} \\), where \\( \\tilde{W}^\\vee = W \\ltimes P \\) (weight lattice). Key constants: rank \\( n \\), torsion primes dividing \\( |W| \\) inverted. No explicit numeric ratios appear — the structure is lattice-theoretic. CONNECTION: Direct link to root systems (crystallographic symmetry). The dual tori \\( T, \\check{T} \\) encode weight vs. coroot lattices — the ratio of their covolumes is the index \\( |P/Q^\\vee| \\) (fundamental group\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ccr7tz9477bq.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23658273",
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  "id": "2ccr7tz9477bq",
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  "landing_url": "https://zenodo.org/records/23658273",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ccr7tz9477bq.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:37Z",
      "native_id": "23658273",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23658273"
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  "subjects": [],
  "title": "Langlands Duality Induces Rational K-Theory Isomorphism for Affine Weyl Groups — E8 Intelligence Research",
  "title_text": "Langlands Duality Induces Rational K-Theory Isomorphism for Affine Weyl Groups — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:37Z",
  "url": "https://research.draconitic.com/paper/2ccr7tz9477bq",
  "venue": "Zenodo",
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}